{
  "id": 2252,
  "curve_key": "864024792153649:-25386772291636124769193",
  "ainvs": [
    "1",
    "0",
    "0",
    "-18000516503201",
    "29382836800461732105"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 103.1778677368296,
  "faltings_height": 6.340732905907319,
  "conductor": "510728790",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "47",
    "149"
  ],
  "discriminant": "312418944674606368957383970520306702400",
  "regulator": "3.975085028077402128395121491014885166634",
  "points": [
    [
      "2392648",
      "105032851"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-47, q=34; A=(3q-p)(p+q)^3=-327353, B=-(p+3q)(p-q)^3=29229255. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.",
  "created_at": "2026-09-26 19:49:54",
  "updated_at": "2026-09-26 19:49:54"
}